We define and study burst-covering codes. We provide some general bounds connecting the code parameters with its burst-covering radius. We then provide stronger bounds on the burst-covering radius of cyclic codes, by employing linear-feedback shift-register (LFSR) sequences. For the case of BCH codes we prove a new bound on pattern frequencies in LFSR sequences, which is of independent interest. Using this tool, we can bound the covering-radius of binary primitive BCH codes and Melas codes. We conclude with an efficient algorithm for burst-covering cyclic codes.

翻译：本文定义并研究了突发覆盖码。我们建立了连接码参数与其突发覆盖半径的若干一般性界。随后，通过利用线性反馈移位寄存器序列，我们为循环码的突发覆盖半径提供了更强的界。针对BCH码的情形，我们证明了关于LFSR序列中模式频率的一个新界，该结果本身具有独立的研究价值。利用这一工具，我们能够界定二进制本原BCH码与Melas码的覆盖半径。最后，我们提出了一种针对突发覆盖循环码的高效算法。